Istanbul 2004 
clusion that the 
uted; the phase 
d intensity with 
ive exponential 
th 4-look are 
1S 1S accordant 
SAR images to 
d calculates the 
ie, such as the 
| pixels output 
ee filter Frost 
oped. Then the 
onsidered. It is 
n(MMSE). The 
1 coefficient. 
as a linear 
imate. The Lee 
(4) 
ve noise model. 
veighting value, 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
* 
T —A*T 
the weighting value is M xe ‚where 
2 
Á m D * (V / / £3 , T is the distance between the pixel 
and central pixel; VIII is respectively the variance and mean of 
filter window. 
Frost filter can be described as followed 
H H 
R2 V (Pi* Mi)/* Mi (5) 
i-l i-l 
where Pi is the pixel's grey value within the filter window. 
3.4 Gamma MAP filter 
Gamma MAP filter is firstly proposed by Kuan. He supposed 
that the probability density distribution of the noise free scene is 
Gauss distributed. But it is not accordant with the real situation. 
Then Lopes correct the filter. He supposed that the PDF of the 
noise free scene and of the noise itself are both Gamma 
distributed. And he set two thresholds for the filter. The filter 
can be described as followed 
I CisCu 
R= (B* I-A D)/Q*a) Cu<Ci<C max 6) 
CP Ci > C max 
where, Cu 1/4 NLook 
Ci=+JVAR/ 1 
Cmax = v2. *Cu 
2 oz 2 
a=(ll+Cu AC —- Cu”) 
B=a-NLook —l 
2 7 t L 
D=F *B 4% * NLook*I*CP 
where, NLOOK is the number of looks; VAR and I are 
respectively the variance and mean of filter window; CP is the 
central pixel's grey value; R is the filtered grey value. 
If the SAR image is single look, the formula should be 
corrected 
  
  
ral alk 
20 
R 7) 
4. The base of forming new filter 
Io form a new filter, we can consider some aspects as followed 
13i 
4.1 Filter kernel 
From analyzing the existing filter algorithms, we can get two 
common formats for the adaptive filters, 
Format 1: La = Li "Wig tm, (1 = Wig) (8) 
] 3. (9) 
"(mat 2- T 
Format 2: T o ij ij 
Where, T is filtered pixel grey value at the center of the 
filter window; I; is the central pixel grey value of the filter 
window; wie is the weighting value calculated from the all 
pixels’ grey value of the filter window; my is the local mean 
calculated from all the pixels of the filter window: lh; is the 
pixel’ grey value within the filter window; wy; is the weighting 
value for every pixel’ grey value within the filter window; * is 
convolution. 
For example, Lee filter and Kuan filter are adopted the Format |. 
And Frost filter is adopted the Format 2. 
4.2 Sub-windows 
We can also divide the filter window to several parts. Every part 
is called sub-window. We can use the sub-window which the 
standard deviation is the least to replace the whole filter window. 
Sub-window can help to improve the ability for preserving 
edges and detecting point targets. There are some dividing 
methods to divide the filter window into several sub windows. 
And different dividing method has different filter effect. So we 
only choose appropriate dividing method, we can filter the 
speckle noise in the SAR images. 
4.3 Threshold 
We can also choose reasonable thresholds to discriminate 
between homogeneous areas, heterogeneous areas and point 
targets. For most practical applications, the thresholds can be 
estimated from the SAR image to be filtered by calculating the 
local mean and the local variance. 
5. A new filter(LogMean) 
This method firstly calculates the logarithm operation to the 
intensity image. By logarithm operation, it can convert the 
multiplicative noise to the additive noise. According to the 
multiplicative noise model, 
Hx, y) 7 Rx, y)* F(x, v) 
It can also be simplified: Jj=R*F 
After logarithm operation, the model is converted: 
In/ =InR+InF (10) 
We can regard InF as the noise, then the noise is additive. We 
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